I have a pc with several partitions which I want to install with custom mount points during installation (all like /media/name_of_my_choice)
Unfortunately the installed doesn't seem to give me the possibility to do that. All I can do is give to partition the usual mount point of / , home, var and so on.
Since it seems impossible to me that there's no such choice available (every other distro I tried ,included Debian installer, let you do that) I'm asking here what am I missing with the installer.

The installer does not handle this, just ignore these partitions at install time and then once you boot into the installed system you can fixup your system for whatever additional mounts you want. If you leave the "mount partitions at boot" option checked all you will actually have to do is:

umount the partitions you want to change
change the mountpoints in fstab from things like /media/disk1part2 to the name you want
rename the directorys like /media/disk1part2 to match what you put in fstab
run "mount -a" to mount them up again as they will be mounted on subsequent boots